Quadratic equation calculator

Quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

3 x^{2} - 4 x + (- 4) = 0 3 x^{2} - 4 x - 4 = 0 a = 3; b = - 4; c = - 4 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 3 \cdot (- 4) = 64 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm 6 4}{6} x_{1, 2} = \frac{4 \pm 8}{6} x_{1, 2} = 0.666667 \pm 1.333333 x_{1} = 2 x_{2} = - 0.666666667 Factored form of the equation: 3 (x - 2) (x + 0.666666667) = 0

Solution in text:

3x²-4x-4=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 64
D > 0 ... The equation has two distinct real roots

x₁ = 2
x₂ = -0.6666667

P = {2; -0.6666667}